This invention relates to an arrangement for the model-based calibration of a robot in a workspace with at least three calibration objects that are either designed to be directed radiation patterns together with associated radiation-pattern generators or radiation-pattern position sensors; when a radiation pattern is encountered, position sensors pass measured values with position information along to the computing devices, which determine the parameters of a mathematical mechanism model with the aid of these measured values.
An arrangement of this type and a method of this type are known to the public from the prior art. First off, fundamental terms will be defined:                1. Mechanism: A mechanism is a system of so-called segments or rigid bodies that are connected to one another via revolute joints, sliding joints or screw joints. Examples are robots, gantries, machine tools or hexapods.        2. Robot: To simplify the understanding of this invention, the term robot 1 will be used as a synonym for the term mechanism below.        3. Effector, or more specifically hand or tool: is a segment of the mechanism that a work object (e.g. grippers (with a workpiece), a milling tool, a camera etc.) can be mounted on for the purpose of carrying out a useful activity. The aim of the invention is to precisely position the effector with the work object in the workspace or relative to the robot base.        4. Pose: describes in a summary fashion the position and orientation of an object in the 3-dimensional ordinary space.        5. Joint configuration: is the totality of all of the positioning values of the joints of a robot that determine the position of all of the robot segments or rigid bodies vis-a-vis one another including the effector.        
The robot is customarily calibrated in advance, i.e. all of the parameters of a mathematical robot model that have an influence on the precision of the effector pose are exactly identified, so that the robot can be precisely controlled in the overall workspace. According to Schröer [Schröer], model-based robot calibration consists of three basic steps in principle:                measurements are performed that provide information on the effector pose of a robot to be calibrated in the workspace;        the measured values that are obtained and the accompanying joint configurations of the robot are correlated with one another via equations for each measurement;        the parameters of a mathematical model of the robot and the pose of the participating calibration objects are calculated from the totality of the equations that are obtained by mathematical methods of parameter identification, for instance by Gauss-Newton methods or Levenberg-Marquardt methods.        
Calibration systems are essentially distinguished by the measurement equipment that is used and the mathematical mechanism model and the mathematical parameter identification algorithms that are used as a basis in each case.
The following terminology definitions will facilitate the entire remaining description:                6. A laser radiation-pattern generator produces directed electromagnetic radiation or directed radiation patterns, for instance individual beams or bundles of isolated individual beams or line-shaped or cross-shaped radiation patterns 9 or any other directed radiation patterns.        7. Laser: For the purposes of simplification, the term laser will be used as a synonym for radiation-pattern generator below.        8. Laser radiation-pattern position sensors can precisely determine the position and orientation, if applicable, of an incident radiation pattern relative to a coordinate system permanently assigned to the sensor. For the purposes of simplification, the term sensor will be used as a synonym for radiation-pattern position sensor below.        9. A calibration object is to be understood to be a generic term for sensors and radiation patterns together with the associated laser in this description. Connected images of radiation patterns on the sensor surface, such as points, lines or crosses, will be considered to be a single calibration object. Unconnected radiation patterns that are generated by a laser, for instance via splitting optics, are considered to be several different calibration objects.        10. A calibration object pair is defined as a connected radiation pattern together with an associated laser and a sensor; one calibration object is attached to the robot effector [“effector object”], and one is stationary in the space [reference object].        11. Laser sensor systems are robot calibration systems that are based on the following principle: A calibration object of a calibration object pair is mounted on the effector and designated as an effector object below. The other calibration object of the pair is positioned in a stationary fashion in or close to the workspace and is designated as a reference object below. The robot moves the effector object into a multitude of poses in which at least one radiation pattern of the laser hits the sensor. The sensor passes the measured values along to the computing unit, which computes the exact parameters of a mathematical mechanism model from the measured values and the associated joint configurations. Calibration object pairs can change in the course of a mechanism calibration or, more precisely: Each laser can irradiate different sensors, and each sensor is irradiated by different radiation patterns.        12. The term initial estimation denominates the initial rough calibration of the calibration objects; see also the notes on FIG. 5 with regard to this. The calibration objects have to be installed—i.e. positioned and mounted—on the robot and in its workcell in practice, and their pose relative to the robot is frequently not exactly known after installation. Before the actual calibration, the poses of the calibration objects have to be determined with sufficient accuracy relative to the robot flange and the robot base in order to generate measurement poses where the laser beams hit the measurement poses of the sensors. The initial, approximate determination of the poses of the calibration objects relative to the robot is called the initial estimation here. Fully automatic initial estimation is difficult from a technical point of view and elaborate in view of the required algorithms and the amount of time required.        13. A functional operation group is a minimal group of calibration objects that fulfill an essential, independent and precisely definable technical function in the process of calibration with laser-sensor systems. The requirement of minimality refers to the number of calibration objects that are involved and means: If one of the calibration objects is removed, the particular functional effect of the group can no longer be fulfilled.                    The most elemental, most simple example of a functional operation group is a customary calibration object pair that is used in the fundamental sense of the instant document or by [P1]. The functional effect involves the collection of measured data in the sense of the fundamental measurement principle here. The characteristic of minimality is fulfilled because the removal of one of the two calibration objects destroys the capability to collect measured data.            A second, important example of a functional operation group is a length standard or etalon as in FIG. 2, for instance, comprised of a laser on the effector and at least two sensors that are mounted at a defined distance on a stationary support unit in accordance with [P1]. No absolute lengths (of robot-arm segments) or distances can be determined via laser-sensor systems at all without a length standard. Length standards consequently have an essential, independent function in the calibration via laser-sensor systems.            FIG. 5 shows, as an example, two functional operation groups: The laser with the sensor that is being hit at the moment constitutes one operation group. The other group is made up of the two other components or calibration objects in FIG. 5. In certain poses, both of them can perform measurements that are synchronous in time.            In FIG. 1, there are four functional operation groups that belong to the sensor that is being irradiated at the moment (formed by the sensor with one of the four laser beams in each case). They can almost always perform simultaneous measurements due to the arrangement. Note that four other functional operation groups belong to this arrangement, namely the same four laser beams that potentially interact with the other sensor in FIG. 1 that is not receiving radiation at the moment.            Of course, it is also possible to rigidly combine several functional operation groups of arbitrary types. E.g. if a rigidly connected isosceles triangle is created from three identical length standards with two sensors each and there is one laser on the effector, as an example, then six elementary functional operation groups are obtained. But six sensors are superfluous—the three sensor pairs at the three connection points in each case can be consolidated or conceptually merged into a single sensor in each case. This results in three functional operation groups with a total of three sensors. Each of the operation groups is a length standard in and of itself! The three length standards are rigidly connected to one another, and each of the total of three sensors belongs to two different length standards in this case.            In the arrangement in FIG. 4, the objects involved in accordance with the definition of the functional operation groups are not                            1. two operation groups with one sensor each and a number of rigidly connected radiation patterns.                                    Rather, this involves                            2. a number of elementary functional operation groups with one sensor and one radiation pattern or laser beam each.                                    Only the second interpretation meets the definition of functional operation groups because                            the combination of two or more laser beams does not fulfill an “essential, independent function” here. All of the beams, aside from one (arbitrary) beam, can be removed from every rigid combination of two or more laser beams without any problems, and the robot can then be calibrated. One only has to make a greater effort and record more measurements, or mount the one laser in other positions on the flange, to get to a comparable calibration result, i.e. only the advantages claimed in this document are lost.                In addition, the requirement of minimality is only fulfilled in the second interpretation.                                                
The fundamentals of laser-sensor methods for industrial use are presented in [P1]. This document is based on [P1] without being limited in its scope by [P1]. The rigid combination of calibration objects in accordance with claim 1 increases the efficiency or benefits of the calibration via laser-sensor systems in different ways. The benefits that result from the rigid combination of calibration objects of various functional operation groups have not been described in any earlier document.
Two methods, among others, for including a length standard or scalar factor in the calibration are presented in a scientific article [Gatla]. The article does not contain any advances vis-a-vis [P1]. The device that is favored in the end moves the robot on a mobile frame by a precise, defined offset, which has little suitability for industrial uses in general. In a second proposal, a rigid combination of lasers and sensors is exclusively investigated for the purpose of determining a scalar factor—thus, the device involves a single length standard or a single functional operation group that is an practically unsuitable variant of the principle from [P1]. The variant in [Gatla] is immediately rejected by the authors because it would lead to a substantial amplification of errors in practice.
[P2] involves a method for measuring the current, specific pose of the effector in each case, in contrast to the calibration of a robot or the identification of the “parameters of a mathematical mechanism model”. The purpose, objectives and method of operation of [P2] are fundamentally different than those of this document. A closer look at [P2] sheds some light on a few of the advantages of the instant invention and concepts, however. If the concept of the functional operation group is applied to effector measurement systems, [P2] involves a system with a single operation group, in so far as a SINGLE “motif lumineux” or a SINGLE “ensemble de taches lumineux” is used here. This document and [P2] are also diametrically opposed to one another with regard to the crucial effect. With a practical realization of [P2], minor measurement errors and minor identification errors can be expected, as is the case with every measurement device, in the determination of the position of the laser beams vis-a-vis one another. The method in [P2] amplifies errors to an extreme degree due to the forced parallelism of the laser beams: If the lasers (motif lumineux) in [P2] are perpendicular over the receiver field (champ de capteur) at a distance of d=1000 mm and if the laser beams are a=30 mm apart from one another and if the overall error (measurement and identification errors) is f=0.01 mm, the resulting error in determining the position is 25.81 mm (=d*arccos(a/(a+f)); thus, the error is amplified by a factor of 2581. The greater the receiver-effector distance, the poorer the determination of the position by [P2]. With an identical implementation, the following will apply to the instant document because of the completely different method of operation: The greater the distance, the better the determination of angles in the robot! To get to the point with regard to the difference, the same measurement that determines a given position with 2500-fold error amplification in accordance with [P2] makes a crucial contribution to the highly precise calibration of the mechanism in accordance with the instant document. The drawbacks of [P2] correspond to the advantages of this invention! One of the objects of this document is to exceed current peak values in robot calibration in the mean-error range of approximately 0.1 to 0.3 mm by a few 1/100 millimeters with an economical apparatus or, as the case may be, to achieve peak results that are more efficient than in the past in terms of accuracy, time consumption and costs.
[P3] and the preceding patents quoted there use stationary sensors and effector-object lasers to derive information about the pose of the effector in various ways over several steps. This device does not serve to calibrate robots either, but instead to measure isolated effector poses. The purpose, aims and method of operation differ from those of this document. The method provides a mathematically proven amplification of errors by a factor of 12 to 13 for a typical industrial robot under optimal conditions. The method, to the extent known, is not used in industry.
Laser sensor pairs are not used for calibration in [P4]. As far as that is concerned, the features of the inventions are different right from the outset. Even if the ball and camera pair from [P4] were equated in some sense with a laser and a sensor, a single functional operation group would be involved as, in particular, none of the cameras could be removed without destroying the functionality of the process.
Laser sensor pairs are not used for measurements in [P5]. As far as that is concerned, the features of the inventions are different right from the outset. Even if cameras and the passive reference objects that are photographed are equated in some sense with lasers and sensors, the apparatus serves to determine the relationship between several cameras and the base of the robot. The concept of calibration is used in the sense of so-called hand-eye coordination here. The objective is not to increase the positioning accuracy of the robot via calibration, but instead to identify the pose of objects or of workpieces relative to the robot via one or more cameras [“accurate machine-workpiece measurements”, “eliminate workpiece pose inaccuracies”]. If a distinction is made between the actual useful production activity of the robot and the calibration process, the cameras in [P5] are used for the precise gripping of objects during the useful production activity of the robot. The mounting positions of the various cameras are determined by the useful activity; they are specified in [P5]. The concept of functional operation groups is not applicable to objects that are predetermined by the useful production activity. In contrast to [P5], the calibration objects in the document in hand are exclusively used for the calibration process, they are part of the apparatus being claimed here or are dependent upon [P1], and their poses are exclusively determined based on considerations involving the calibration process. The advantages of the rigid combination of calibration objects that are crucial for the instant invention are not described in [P5].
The drawbacks of previous laser-sensor methods for the model-based calibration of robots are, above all:                They provide little information per measurement and require too many time-consuming measurements for critical applications, for instance so-called temperature compensation;        The average pose accuracy of the calibrated robot remains low in the overall workspace because of the use of a single calibration object pair. When more than two calibration objects are used, in contrast, the number of parameters to be identified increases because the poses of all of the calibration objects have to be precisely determined without fail, which likewise decreases the resulting effector-pose accuracy of the calibrated mechanism;        The installation of several calibration objects on the robot and in the workspace of the robot for the purpose of laser-sensor calibration is complex and requires experience.        The initial estimation of several calibration objects is technically complex and time-consuming:        The clearance in the workcell that is required for calibration is large.        